We present new complexity results on the class of 0/1/All constraints. The central idea involves functional elimination, a general method of elimination whose focus is on the subclass of functional constraints. One result is that for the subclass of 'All' constraints, strong n-consistency and minimality is achievable in O(en) time, where e, n are the number of constraints and variables. The main result is that we can solve 0/1/All constraints in O(e(d + n)) time, where d is the domain size. This is an improvement over known results, which are O(ed(d + n)). Furthermore, our algorithm also achieves strong n-consistency and minimality.